/*
 * Copyright 2010-2012 Susanta Tewari. <freecode4susant@users.sourceforge.net>
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

package bd.org.apache.commons.math.special;

import bd.org.apache.commons.math.util.FastMath;

/**
 * This is a utility class that provides computation methods related to the
 * error functions.
 *
 * @version $Id: Erf.java 1244107 2012-02-14 16:17:55Z erans $
 */
public class Erf {

    /**
     * The number {@code X_CRIT} is used by {@link #erf(double, double)} internally.
     * This number solves {@code erf(x)=0.5} within 1ulp.
     * More precisely, the current implementations of
     * {@link #erf(double)} and {@link #erfc(double)} satisfy:<br/>
     * {@code erf(X_CRIT) < 0.5},<br/>
     * {@code erf(Math.nextUp(X_CRIT) > 0.5},<br/>
     * {@code erfc(X_CRIT) = 0.5}, and<br/>
     * {@code erfc(Math.nextUp(X_CRIT) < 0.5}
     */
    private static final double X_CRIT = 0.4769362762044697;

    /**
     * Default constructor.  Prohibit instantiation.
     */
    private Erf() {}

    /**
     * Returns the error function.
     * <p>erf(x) = 2/&radic;&pi; <sub>0</sub>&int;<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p>
     * <p>This implementation computes erf(x) using the
     * {@link Gamma#regularizedGammaP(double, double, double, int) regularized gamma function},
     * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p>
     * <p>The value returned is always between -1 and 1 (inclusive).
     * If {@code abs(x) > 40}, then {@code erf(x)} is indistinguishable from
     * either 1 or -1 as a double, so the appropriate extreme value is returned.
     * </p>
     *
     * @param x the value.
     * @return the error function erf(x)
     * @see Gamma#regularizedGammaP(double, double, double, int)
     */
    public static double erf(double x) {

        if (FastMath.abs(x) > 40) {

            return (x > 0)
                   ? 1
                   : -1;
        }

        final double ret = Gamma.regularizedGammaP(0.5, x * x, 1.0e-15, 10000);

        return (x < 0)
               ? -ret
               : ret;
    }


    /**
     * Returns the complementary error function.
     * <p>erfc(x) = 2/&radic;&pi; <sub>x</sub>&int;<sup>&infin;</sup> e<sup>-t<sup>2</sup></sup>dt
     * <br/>
     * = 1 - {@link #erf(double) erf(x)} </p>
     * <p>This implementation computes erfc(x) using the
     * {@link Gamma#regularizedGammaQ(double, double, double, int) regularized gamma function},
     * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p>
     * <p>The value returned is always between 0 and 2 (inclusive).
     * If {@code abs(x) > 40}, then {@code erf(x)} is indistinguishable from
     * either 0 or 2 as a double, so the appropriate extreme value is returned.
     * </p>
     *
     * @param x the value
     * @return the complementary error function erfc(x)
     * @see Gamma#regularizedGammaQ(double, double, double, int)
     * @since 2.2
     */
    public static double erfc(double x) {

        if (FastMath.abs(x) > 40) {

            return (x > 0)
                   ? 0
                   : 2;
        }

        final double ret = Gamma.regularizedGammaQ(0.5, x * x, 1.0e-15, 10000);

        return (x < 0)
               ? 2 - ret
               : ret;
    }


    /**
     * Returns the difference between erf(x1) and erf(x2).
     * The implementation uses either erf(double) or erfc(double)
     * depending on which provides the most precise result.
     *
     * @param x1 the first value
     * @param x2 the second value
     * @return erf(x2) - erf(x1)
     */
    public static double erf(double x1, double x2) {

        if (x1 > x2) {
            return -erf(x2, x1);
        }

        return (x1 < -X_CRIT)
               ? (x2 < 0.0)
                 ? erfc(-x2) - erfc(-x1)
                 : erf(x2) - erf(x1)
               : ((x2 > X_CRIT) && (x1 > 0.0))
                 ? erfc(x1) - erfc(x2)
                 : erf(x2) - erf(x1);
    }
}
